Skip to main content
SpringerLink
Log in

One-Way Repeated Measures ANOVA for Functional Data

  • Conference paper
  • First Online:
Data Analysis and Rationality in a Complex World (IFCS 2019)

Included in the following conference series:

  • 867 Accesses

Abstract

In this paper, the one-way repeated measures analysis of variance for functional data is considered. For this problem, the new test statistics are obtained by integrating and taking supremum of the constructed pointwise test statistic. To approximate the null distributions of the test statistics and construct the testing procedures, different bootstrap and permutation methods are used. The performance of the new tests and their comparisons with the known testing procedures in terms of size control and power is established in simulation studies. These studies indicate that the new tests may have different finite sample properties, but they are usually more powerful than the tests proposed in the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Ferraty, F., Vieu, P.: Nonparametric Functional Data Analysis: Theory and Practice. Springer, New York (2006)

    MATH  Google Scholar 

  • Horváth, L., Kokoszka, P.: Inference for Functional Data with Applications. Springer, New York (2012)

    Book  Google Scholar 

  • Kokoszka, P., Reimherr, M.: Introduction to Functional Data Analysis. Chapman and Hall/CRC (2017)

    Google Scholar 

  • Konietschke, F., Pauly, M.: Bootstrapping and permuting paired \(t\)-test type statistics. Stat. Comput. 24, 283–296 (2014)

    Article  MathSciNet  Google Scholar 

  • Konietschke, F., Bathke, A.C., Harrar, S.W., Pauly, M.: Parametric and nonparametric bootstrap methods for general MANOVA. J. Multivar. Anal. 140, 291–301 (2015)

    Article  MathSciNet  Google Scholar 

  • Martínez-Camblor, P., Corral, N.: Repeated measures analysis for functional data. Comput. Stat. Data Anal. 55, 3244–3256 (2011)

    Article  MathSciNet  Google Scholar 

  • R Core Team: R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria (2019). https://www.R-project.org/

  • Ramsay, J.O., Silverman, B.W.: Applied Functional Data Analysis. Methods and Case Studies. Springer, New York (2002)

    Google Scholar 

  • Ramsay, J.O., Silverman, B.W.: Functional Data Analysis, 2nd edn. Springer, New York (2005)

    Book  Google Scholar 

  • Smaga, Ł.: Repeated measures analysis for functional data using Box-type approximation—with applications. REVSTAT 17(4), 523–549 (2019a)

    Google Scholar 

  • Smaga, Ł.: A note on repeated measures analysis for functional data. AStA Adv. Stat. Anal. 104(1), 117–139 (2019b)

    Google Scholar 

  • Zhang, J.T., Liang, X.: One-way ANOVA for functional data via globalizing the pointwise \(F\)-test. Scand. J. Stat. 41, 51–71 (2014)

    Google Scholar 

  • Zhang, J.T.: Analysis of Variance for Functional Data. Chapman and Hall, London (2013)

    Book  Google Scholar 

  • Zhang, J.T., Cheng, M.Y., Wu, H.T., Zhou, B.: A new test for functional one-way ANOVA with applications to ischemic heart screening. Comput. Stat. Data Anal. 132, 3–17 (2019)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Uniwersytetu Poznańskiego 4, 61-614, Poznań, Poland

    Łukasz Smaga

Authors
  1. Łukasz Smaga
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Łukasz Smaga .

Editor information

Editors and Affiliations

  1. Department of Political Sciences, Aristotle University of Thessaloniki, Thessaloniki, Greece

    Theodore Chadjipadelis

  2. Department of Mathematical Sciences, University of Essex, Colchester, UK

    Berthold Lausen

  3. School of Education, Democritus University of Thrace, Alexandroupolis, Greece

    Angelos Markos

  4. Department of Data Science and Statistics, Korea National Open University, Seoul, Korea (Republic of)

    Tae Rim Lee

  5. Department of Statistical Sciences “Paolo Fortunati”, University of Bologna, Bologna, Italy

    Angela Montanari

  6. Department of Statistics and Data Science, Carnegie Mellon University, Pittsburgh, PA, USA

    Rebecca Nugent

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Smaga, Ł. (2021). One-Way Repeated Measures ANOVA for Functional Data. In: Chadjipadelis, T., Lausen, B., Markos, A., Lee, T.R., Montanari, A., Nugent, R. (eds) Data Analysis and Rationality in a Complex World. IFCS 2019. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-030-60104-1_27

Download citation

Publish with us

Policies and ethics

Search

Navigation